Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\sqrt[3]{{\left(\frac{x + 1}{1 - x}\right)}^{3}}\]
\frac{x + 1}{1 - x}
↓
\sqrt[3]{{\left(\frac{x + 1}{1 - x}\right)}^{3}}
double f(double x) {
        double r38698 = x;
        double r38699 = 1.0;
        double r38700 = r38698 + r38699;
        double r38701 = r38699 - r38698;
        double r38702 = r38700 / r38701;
        return r38702;
}
↓
double f(double x) {
        double r38703 = x;
        double r38704 = 1.0;
        double r38705 = r38703 + r38704;
        double r38706 = r38704 - r38703;
        double r38707 = r38705 / r38706;
        double r38708 = 3.0;
        double r38709 = pow(r38707, r38708);
        double r38710 = cbrt(r38709);
        return r38710;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{x + 1}{1 - x}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube21.3

    \[\leadsto \frac{x + 1}{\color{blue}{\sqrt[3]{\left(\left(1 - x\right) \cdot \left(1 - x\right)\right) \cdot \left(1 - x\right)}}}\]

  4. Applied add-cbrt-cube21.9

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(x + 1\right) \cdot \left(x + 1\right)\right) \cdot \left(x + 1\right)}}}{\sqrt[3]{\left(\left(1 - x\right) \cdot \left(1 - x\right)\right) \cdot \left(1 - x\right)}}\]

  5. Applied cbrt-undiv21.9

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\left(x + 1\right) \cdot \left(x + 1\right)\right) \cdot \left(x + 1\right)}{\left(\left(1 - x\right) \cdot \left(1 - x\right)\right) \cdot \left(1 - x\right)}}}\]

  6. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{x + 1}{1 - x}\right)}^{3}}}\]

  7. Final simplification0.0

    \[\leadsto \sqrt[3]{{\left(\frac{x + 1}{1 - x}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020025 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))